2003 AMC amc12b 真题 答案 详解

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英文真题

2003 AMC 12B Problems Problem 1 Which of the following is the same as $$\frac{2-4+6-8+10-12+14}{3-6+9-12+15-18+21}$$? (A) -1 (B) -\frac{2}{3} (C) \frac{2}{3} (D) 1 (E) \frac{14}{3} Problem 2 Al gets the disease algebritis and must take one green pill and one pink pill each day for two weeks. A green pill costs 1 dollar more than a pink pill, and Al's pills cost a total of 546 dollars for the two weeks. How much does one green pill cost? (A) 7 (B) 14 (C) 19 (D) 20 (E) 39 Problem 3 Rose fills each of the rectangular regions of her rectangular flower bed with a different type of flower. The lengths, in feet, of the rectangular regions in her flower bed are as shown in the figure. She plants one flower per square foot in each region. Asters cost $1 each, begonias $1.50 each, cannas $2 each, dahlias $2.50 each, and Easter lilies $3 each. What is the least possible cost, in dollars, for her garden? (A) 108 (B) 115 (C) 132 (D) 144 (E) 156 Problem 4 Moe uses a mower to cut his rectangular 90-foot by 150-foot lawn. The swath he cuts is 28 inches wide, but he overlaps each cut by 4 inches to make sure that no grass is missed. He walks at the rate of 5000 feet per hour while pushing the mower. Which of the following is closest to the number of hours it will take Moe to mow his lawn? (A) 0.75 (B) 0.8 (C) 1.35 (D) 1.5 (E) 3 Problem 5 Many television screens are rectangles that are measured by the length of their diagonals. The ratio of the horizontal length to the height in a standard television screen is 4:3. The horizontal length of a "27-inch" television screen is closest, in inches, to which of the following? (A) 20 (B) 20.5 (C) 21 (D) 21.5 (E) 22 Problem 6 The second and fourth terms of a geometric sequence are 2 and 6. Which of the following is a possible first term? (A) -\sqrt{3} (B) \frac{-2\sqrt{3}}{3} (C) \frac{-\sqrt{3}}{3} (D) \sqrt{3} (E) 3 Problem 7 Penniless Pete's piggy bank has no pennies in it, but it has 100 coins, all nickels, dimes, and quarters, whose total value is $8.35. It does not necessarily contain coins of all three types. What is the difference between the largest and smallest number of dimes that could be in the bank? (A) 0 (B) 13 (C) 37 (D) 64 (E) 83 Problem 8 Let $\clubsuit(x)$ denote the sum of the digits of the positive integer $x$. For example, $\clubsuit(8)=8$ and $\clubsuit(123)=1+2+3=6$. For how many two-digit values of $x$ is $\clubsuit(\clubsuit(x))=3$? (A) 3 (B) 4 (C) 6 (D) 9 (E) 10

真题文字详解(英文)

Problem 1 The following problem is from both the 2003 AMC 12B #1 and 2003 AMC 10B #1, so both problems redirect to this page. Which of the following is the same as $$\frac{2-4+6-8+10-12+14}{3-6+9-12+15-18+21}$$? (A) -1 (B) $-\frac{2}{3}$ (C) $\frac{2}{3}$ (D) 1 (E) $\frac{14}{3}$ Solution 1 $$\frac{2-4+6-8+10-12+14}{3-6+9-12+15-18+21}=\frac{2+(-4+6)+(-8+10)+(-12+14)}{3+(-6+9)+(-12+15)+(-18+21)}=\frac{2\cdot4}{3\cdot4}=(C)\frac{2}{3}$$ Solution 2 Each term in the numerator is $(C)\frac{2}{3}$ of a corresponding term in the denominator, so this must be the quotient. See also Problem 2 The following problem is from both the 2003 AMC 12B #2 and 2003 AMC 10B #2, so both problems redirect to this page. Al gets the disease algebritis and must take one green pill and one pink pill each day for two weeks. A green pill costs $1 more than a pink pill, and Al's pills cost a total of $546 for the two weeks. How much does one green pill cost? (A) $7 (B) $14 (C) $19 (D) $20 (E) $39 Solution Because there are 14 days in two weeks, Al spends 546/14 = 39 dollars per day for the cost of a green pill and a pink pill. If the green pill costs x dollars and the pink pill x - 1 dollars, the sum of the two costs 2x - 1 should equal 39 dollars. Then the cost of the green pill x is (D) $20 Problem 3 The following problem is from both the 2003 AMC 12B #3 and 2003 AMC 10B #4, so both problems redirect to this page. Rose fills each of the rectangular regions of her rectangular flower bed with a different type of flower. The lengths, in feet, of the rectangular regions in her flower bed are as shown in the figure. She plants one flower per square foot in each region. Asters cost $1 each, begonias $1.50 each, cannas $2 each, dahlias $2.50 each, and Easter lilies $3 each. What is the least possible cost, in dollars, for her garden?

真题文字详解(中英双语)

Problem 1 The following problem is from both the 2003 AMC 12B #1 and 2003 AMC 10B #1, so both problems redirect to this page. 以下问题既来自2003年AMC 12B #1，也来自2003年AMC 10B #1，因此这两个问题都重定向到此页面。 Which of the following is the same as (\frac{2-4+6-8+10-12+14}{3-6+9-12+15-18+21})? (A) -1 (B) (-\frac{2}{3}) (C) (\frac{2}{3}) (D) 1 (E) (\frac{14}{3})

Solution 1 (\frac{2-4+6-8+10-12+14}{3-6+9-12+15-18+21} = \frac{2 + (-4+6)+(-8+10)+(-12+14)}{3+(-6+9)+(-12+15)+(-18+21)} = \frac{2 \cdot 4}{3 \cdot 4} = (C)\frac{2}{3})

Solution 2 Each term in the numerator is (C) (\frac{2}{3}) of a corresponding term in the denominator, so this must be the quotient. 分子中的每一项都是相应分母中项的(C) (\frac{2}{3})，因此这必须是商。

See also Problem 2 The following problem is from both the 2003 AMC 12B #2 and 2003 AMC 10B #2, so both problems redirect to this page. 以下问题既来自2003年AMC 12B #2，也来自2003年AMC 10B #2，因此这两个问题都重定向到此页面。 Al gets the disease algebritis and must take one green pill and one pink pill each day for two weeks. A green pill costs $1 more than a pink pill, and Al's pills cost a total of $546 for the two weeks. How much does one green pill cost? 阿尔得了叫做algebritis的病，必须每天服用一粒绿色药丸和一粒粉色药丸，持续两周。绿色药丸的价格比粉色药丸贵$1，阿尔两周的药费总共是$546。一粒绿色药丸的价格是多少？ (A) $7 (B) $14 (C) $19 (D) $20 (E) $39 Solution Because there are 14 days in two weeks, Al spends $546/14 = $39 dollars per day for the cost of a green pill and a pink pill. If the green pill costs x dollars and the pink pill x - 1 dollars, the sum of the two costs 2x - 1 should equal 39 dollars. Then the cost of the green pill is (D) $20. 因为两周有14天，阿尔每天花费$546/14=$39美元购买绿色药丸和粉色药丸。如果绿色药丸的价格是x美元，粉色药丸的价格是x-1美元，那么两种药丸的总成本2x-1应该等于39美元。那么绿色药丸的成本x是(D)$20。